We studied surface morphology and magnetic properties of Fe/MgO(001) films deposited at an angle varying between 0 degrees and 60 degrees with respect to the surface normal and with azimuth along the Fe[010] or the Fe[110] direction. Due to shadowing, elongated grains appear on the film surface for deposition at sufficiently large angle. X-ray reflectivity reveals that, depending on the azimuthal direction, films become either rougher or smoother for oblique deposition. For deposition along Fe[010] the pronounced uniaxial magnetic anisotropy (UMA) results in the occurrence of "reversed" two-step and of three-step hysteresis loops. For deposition along Fe[110] the growth-induced UMA is much weaker, causing a small rotation of the easy axes.